Project #33493 - Probability/Statistics

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1.) The variance of a binomial distribution for which n = 100 and p = 0.20 is:

2.) The atoms of a radioactive element are randomly disintegrating. The process can be modeled with a Poisson distribution. Every gram of this element, on average, emits 3.9 alpha particles per second. Find the probability that during the next second the number of alpha particles emitted from 1 gram is:

At most 6:

Between 3 and 6 included:

3.) A recent survey in Michigan revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on a Michigan highway where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit.

What is the probability that no cars are exceeding the speed limit?

What is the probability that at least 7 cars are exceeding the speed limit?

Suppose that an highway patrol officer can obtain radar readings on 500 vehicles during a typical shift. How many traffic violations would be found in a shift?

4.) Consider two random variables X and Y. Suppose that the variance of X is 20, that this of Y is 10, and that the covariance of X and Y is 5. What is the variance of the random variable 2X+Y?

5.) Half of all newborns are girls and half are boys. Hospital A records an average of 50 births a day. Hospital B records an average of 10 births a day. On a particular day, which hospital is more likely to record 80% or more female births?

6.) A corporate executive officer is attempting to arrange a meeting of his three vice presidents for tomorrow morning. He believes that each of these three busy persons, independently of the others, has about a 60% chance of being able to attend the meeting. What is the probability that exactly two of the three vice presidents can attend the meeting?